No gravity at center of earth= no pressure?

[D H]

Mailbuguy, you have been given several pointers to read. Have you read any of them? Please read:

• Newton's shell theorem, http://en.wikipedia.org/wiki/Shell_theorem
• Gauss' law, http://en.wikipedia.org/wiki/Gauss'_law_for_gravity
• Preliminary Earth Reference Model, http://geophysics.ou.edu/solid_earth/prem.html

You (and others) are confusing force and energy. These are related but different concepts. Gravitational force is zero at the center of the Earth. Gravitational energy is a different story. It is energy, not force, that explains why planets become differentiated. Nature seeks a minimum energy configuration.

 

[Malibuguy]

Just looking at the fact that a lot of planets have a dense core of metal and are not homogeneous.

The other perspective is that it is the surface pushing in on all sides.
But then this will produce a center that is more dense. A denser center produces gravity too.
The surface of this denser center pushes in on all sides too and then this creates more pressure. Then you get an inner core which is hotter and more dense Which is exactly what we have with the earth. This center also produces gravity. If one follows this idea then there will always be gravity at the center of the earth.

 

[Malibuguy]

Newtons shell assumes homogenious shell. Newtons shell seeks to explain our world one aspect .

But our world is not a homogenious shell. Neither is the moon Jupiter and a lot of other planets.

Please find a large body in the universe which produces significant gravity and is homogenious without a dense core

 

[Doc Al]

The other perspective is that it is the surface pushing in on all sides.
But then this will produce a center that is more dense. A denser center produces gravity too.
The surface of this denser center pushes in on all sides too and then this creates more pressure. Then you get an inner core which is hotter and more dense Which is exactly what we have with the earth. This center also produces gravity. If one follows this idea then there will always be gravity at the center of the earth.

Nope, still wrong. Any mass at the center of the Earth (say within some small radius r) only contributes to the gravity for distances from the center greater than r. At the very center the gravitational field strength is zero.

 

[sophiecentaur]

Newtons shell assumes homogenious shell. Newtons shell seeks to explain our world one aspect .

But our world is not a homogenious shell. Neither is the moon Jupiter and a lot of other planets.

Please find a large body in the universe which produces significant gravity and is homogenious without a dense core

The fact that a planet gets more dense towards the centre doesn't invalidate the assumption that it can be (more or less ) spherically symmetrical). Newton's shell theory deals with one uniform shell at a time. Its result is not affected by the density increasing with depth.;

But why not take one thing at a time? The original question was addressed using the most simple assumption (uniform density). People seemed to have enough difficulties dealing with that basic model but I think we got there more or less.
The next step is to allow the more dense stuff to gravitate towards the centre. That gives a more complicated result - slightly counter to the original but makes sense.

If you want to have asymmetry too then you'd have to modify the result further but, to what end? The basic principles tend to get lost in the specific instances in the end. But, whatever you suggest as a possible model, there will be somewhere 'in there' where the Potential is at a minimum and the force is zero.

 

[Malibuguy]

At the very center? What is that a point of one dimension? A place that has no volume That's not even a place. Hmm but maybe you mean that the net gravitational force is zero. What about the field of gravity around a volume located at the center?

 

[Doc Al]

Newtons shell assumes homogenious shell. Newtons shell seeks to explain our world one aspect .

But our world is not a homogenious shell. Neither is the moon Jupiter and a lot of other planets.

Please find a large body in the universe which produces significant gravity and is homogenious without a dense core

Sure, if a spherical mass has a lopsided mass distribution, there may well be a non-zero field at the geometric center. This has nothing to do with a 'dense core'.

 

[Doc Al]

At the very center? What is that a point of one dimension? A place that has no volume That's not even a place. Hmm but maybe you mean that the net gravitational force is zero. What about the field of gravity around a volume located at the center?

Again, for a spherically symmetric mass distribution, the field around some volume at the center is due to the mass contained within that volume. Regardless of the density of the core, as you get closer to the center the field goes to zero.

 

[sophiecentaur]

At the very center? What is that a point of one dimension? A place that has no volume That's not even a place. Hmm but maybe you mean that the net gravitational force is zero. What about the field of gravity around a volume located at the center?

For a small volume, the range of potential would be small, If you want to be picky, you could call it a situation of 'microgravity' rather than zero gravity - similar to that experienced in an orbiting spacecraft , in which objects are only weightless around the CM of the craft and payload. On either side of this, there is not zero weight but a finite force.

The way it's been approached in this thread is consistent with the normal way of getting to grips with basics - start with the simplest model and add complications later.

 

[Drakkith]

How's this sophie? The net force of gravity is zero at the center of the earth. The FORCE of gravity combines to equal out in every direction, just like pushing in on all sides of a box with equal force results in no net force in a direction.

 

[cragar]

That is a deep philosophical point. Isn't it all a man-made invention? Fields are only a way of interpreting what we see happening to things. The whole thing can be looked at in terms of Energy just as well. You can never say what things 'really' are. You can only use models and the Force model may have its appeal to you because it sort of feels right - nothing more.

Try some QM using forces alone - that could prove tricky.

I don't think it is philosophical at all. When I'm in a field there is energy in that field for me to interact with. So if I am in the center of Earth is there energy from the gravitational field, not counting my own field. How could my clock tell the difference between being in a place where the field canceled to be zero or where the field was zero because there was no energy around. If there is no energy around I don't see how my clock could tell the difference.

 

[DaveC426913]

I don't think it is philosophical at all. When I'm in a field there is energy in that field for me to interact with. So if I am in the center of Earth is there energy from the gravitational field, not counting my own field. How could my clock tell the difference between being in a place where the field canceled to be zero or where the field was zero because there was no energy around. If there is no energy around I don't see how my clock could tell the difference.

By definition, a field has a value everywhere. That value may be zero in some places, but the point is that at the centre of the Earth, an object does indeed interact with the gravitational field, a field which extends to infinity.

 

[Malibuguy]

I was also interested in the kinds of conditions where gravity would be its greatest.

Someone suggested a black hole. And a black hole would have a huge mass occupying a very small volume something like Jupiter but the size of a speck of dust.

So the center of the speck would have zero gravity and zero pressure?

 

[Drakkith]

I was also interested in the kinds of conditions where gravity would be its greatest.

Someone suggested a black hole. And a black hole would have a huge mass occupying a very small volume something like Jupiter but the size of a speck of dust.

So the center of the speck would have zero gravity and zero pressure?

No, the singularity of a black hole has zero volume and infinite density. There is no center of a singularity in those conditions.

 

[sophiecentaur]

How's this sophie? The net force of gravity is zero at the center of the earth. The FORCE of gravity combines to equal out in every direction, just like pushing in on all sides of a box with equal force results in no net force in a direction.

That makes perfect sense because you use the term Force of Gravity, which removes ambiguity. I think you would agree that a statement about an 'electrical' situation that talked about "electricity in a wire" could introduce confusion. You would want to know whether Current, Charge, Voltage or Power was being referred to.
My problem was with the generic word "gravity".
There is nothing special about the addition (integral) of all forces on an object at the centre of a planet. The effect of gravity is always the sum of all the forces. On the surface, you are being pulled in all directions (particularly in the 'downward' hemisphere) by all constituent parts of the planet. The resultant happens to be vertically downwards (towards the centre of mass). For other, non-spherical, shapes, the CM will not always be the point of attraction.

 

[sophiecentaur]

I was also interested in the kinds of conditions where gravity would be its greatest.

Someone suggested a black hole. And a black hole would have a huge mass occupying a very small volume something like Jupiter but the size of a speck of dust.

So the center of the speck would have zero gravity and zero pressure?

Despite what has been written all through this thread, you are still, somehow, wanting pressure to be linked, inexorably, to gravity. Whilst you can say that pressure is often caused by gravitational attraction, it can, at least in principle, be protected against - where gravitational forces of course cannot. Moreover, you can generate high pressure in conditions involving very low gravitational fields.

 

[DaveC426913]

...a huge mass occupying a very small volume something like Jupiter but the size of a speck of dust.

To be accurate: something like 3x the size of the sun at a minimum, but with theoretically zero volume.

So the center of the speck would have zero gravity and zero pressure?

No. The center of the BH is beyond currently understood physics.

 

[sophiecentaur]

I don't think it is philosophical at all. When I'm in a field there is energy in that field for me to interact with. So if I am in the center of Earth is there energy from the gravitational field, not counting my own field. How could my clock tell the difference between being in a place where the field canceled to be zero or where the field was zero because there was no energy around. If there is no energy around I don't see how my clock could tell the difference.

How do you 'Know' the gravitational field is there? You may be aware of having measured or experienced a force in the place you are standing but it is a complete act of faith that there is actually something one metre to the right. That Vector Field we all believe in is only there when we actually measure it - when there is some object for it to act on. Of course I believe in fields but only because they are a good model to work with. And why should a (vector) gravitational field be any more 'real' than a scalar field like gravitational potential? I think your initial response shows that you may need to think about things more deeply. Nothing is 'obvious'.

Did you ever consider that, whilst You are in the Earth's gravitational field and you Weigh a certain amount, the Earth is also in Your gravitational field. SO, are there two fields? Is it the two fields interacting or is it 'just' a force between two things? Or is it all 'just the way we look at things'?

Now tell me there's no Philosophy involved.

 

[Drakkith]

That makes perfect sense because you use the term Force of Gravity, which removes ambiguity. I think you would agree that a statement about an 'electrical' situation that talked about "electricity in a wire" could introduce confusion. You would want to know whether Current, Charge, Voltage or Power was being referred to.
My problem was with the generic word "gravity".
There is nothing special about the addition (integral) of all forces on an object at the centre of a planet. The effect of gravity is always the sum of all the forces. On the surface, you are being pulled in all directions (particularly in the 'downward' hemisphere) by all constituent parts of the planet. The resultant happens to be vertically downwards (towards the centre of mass). For other, non-spherical, shapes, the CM will not always be the point of attraction.

I already explained that in post # 93 and #95. For some reason I suddenly had you and doc questioning what I was explaining. It's so confusing!

 

[cragar]

How do you 'Know' the gravitational field is there? You may be aware of having measured or experienced a force in the place you are standing but it is a complete act of faith that there is actually something one metre to the right. That Vector Field we all believe in is only there when we actually measure it - when there is some object for it to act on. Of course I believe in fields but only because they are a good model to work with. And why should a (vector) gravitational field be any more 'real' than a scalar field like gravitational potential? I think your initial response shows that you may need to think about things more deeply. Nothing is 'obvious'.

Did you ever consider that, whilst You are in the Earth's gravitational field and you Weigh a certain amount, the Earth is also in Your gravitational field. SO, are there two fields? Is it the two fields interacting or is it 'just' a force between two things? Or is it all 'just the way we look at things'?

Now tell me there's no Philosophy involved.

ok, maybe I should go think about it some more.

 

[cragar]

@ Drakkith , when you said that if your in the center of a hollow cavity in the earth, you still attract everything around you. I guess we could say that if you exert a force on the Earth around you, then it exerts a force on you as well. Or maybe I am over simplifying it.

 

[Drakkith]

@ Drakkith , when you said that if your in the center of a hollow cavity in the earth, you still attract everything around you. I guess we could say that if you exert a force on the Earth around you, then it exerts a force on you as well. Or maybe I am over simplifying it.

It's easy cragar. Every particle exerts gravitational force on every other particle, with increasing strength as they get closer to each other. That's all it is right there. Everything else just builds on that one piece. Pressure is simply how much force you have to exert against those particles to keep them from getting closer together. The complicated part is adding in more particles.

I think the biggest problem in this thread has been incorrect use of terms. You ALWAYS experience the force from an object. If you have an equal amount of force pushing or pulling you in every direction you have no NET force, which means that you won't be pushed or pulled from your current position, but the forces are still pushing or pulling on you.

 

[Avijeet]

To calculate the pressure you have to consider an infinitesimal area element around the center of the Earth and calculate the force acting on it per unit area. To get the value at the center of the earth, we need to take the infinitesimal limit of the above quantity, which need not be zero.

 

[Drakkith]

To calculate the pressure you have to consider an infinitesimal area element around the center of the Earth and calculate the force acting on it per unit area. To get the value at the center of the earth, we need to take the infinitesimal limit of the above quantity, which need not be zero.

What?

 

[cragar]

It's easy cragar. Every particle exerts gravitational force on every other particle, with increasing strength as they get closer to each other. That's all it is right there. Everything else just builds on that one piece. Pressure is simply how much force you have to exert against those particles to keep them from getting closer together. The complicated part is adding in more particles.

I think the biggest problem in this thread has been incorrect use of terms. You ALWAYS experience the force from an object. If you have an equal amount of force pushing or pulling you in every direction you have no NET force, which means that you won't be pushed or pulled from your current position, but the forces are still pushing or pulling on you.

ok I see what you are saying.

 

[treehouse]

Being in the center of an object's gravitational field means being where it is densest. So you would be closer and more affected by the gravitational fields of its densest components. You would have the all attractive forces of all the parts of the object centered on you.

 

[DaveC426913]

Corrected:

Being in the center of an object's gravitational field usually means being where it is densest.

It is certainly not the case for the hollow spheres we are often referring to here.

You would have the all attractive forces of all the parts of the object centered on you.

I do not know what this means. It sounds like a sloppy use of terms.

 

[Malibuguy]

Well the center of the Earth has been further subclassified as have an "inner inner core"
The outer core is liquid iron and the inner core a solid but very hot iron. The extreme pressure of the inner core is counter acted by the high temperature. When the inner core cools a little it will probably change and perhaps the solid metal will shrink in size and grow more dense.

Neutrons have been observed to ascend to a quantum higher level when exposed to gravitational field. The quantum character of these neutron states may provide some explanation why objects fall at the same rate.

But it would be nice to know what happens to the Neutron when it has come to rest on the earth. Do the close proximity of neutrons to other neutrons generate gravity? Denser materials have more neutrons and generate more gravity? Can gravity byitself change atoms so the the electron cloud can get pushed out and neutron and protons get closer together ?

 

[Drakkith]

But it would be nice to know what happens to the Neutron when it has come to rest on the earth. Do the close proximity of neutrons to other neutrons generate gravity? Denser materials have more neutrons and generate more gravity?

A free neutron doesn't "come to rest" in the earth. The uncharged nature of the neutron means that it does not interact with electrons and only interacts with protons when it gets very very close and is at the right velocity to be captured into the nucleus, if possible. Otherwise they pass through most materials and "bounce" off the nucleus, losing speed each time. Every 15 minutes outside of the nucleus of an atom, a neutron has a 50% chance of decaying into a proton. The only exception is extreme gravity such as in a Neutron star.

Anyways, your view suggests that neutrons exert gravity but not other matter? If so this is entirely false, as a quick look at the Sun will show you. All matter, protons and electrons included, generate a gravitational field. In fact, all mass generates a gravitational field along with "massless" photons since they have momentum.

Can gravity byitself change atoms so the the electron cloud can get pushed out and neutron and protons get closer together ?

I don't know what you mean by this.

 

[Malibuguy]

Thanks. No I wasn't implying that a free neutron comes to
Rest on the earth. I was thinking about the object that comes to rest on the Earth now becomes part if the gravitational mass of the earth. What happens to the quantum state of the neutrons?

I wasn't implying that neutrons are the only thing that create gravity. I was just trying to talk about some interesting possibilities due to what is known about neutrons.

As far as electron clouds go , I was trying to get a better idea of what happens to the iron or other matter when it becomes hyperdense. In order to increase density one has to get the neutrons and protons closer together. Neighboring atoms might getnso close that their electron clouds might get distorted or maybe the electron and proton would meet and annihilate.

 

[Drakkith]

Ah, I see what you are saying now. I have to ask though, where did you hear about some quantum state of neutrons changing in a gravitiational field? I've never heard of that before.

 

[Malibuguy]

There was a study done you can google neutrons and gravity field.

But the idea of super dense matter , to me , implies changes to the atomic structure. There is a lot of empty space in an atom with the
Distance of the electrons and maybe even the space
Within a neutron or proton

 

[ZealScience]

Though you would have no effect of gravity, but the outer layer is NOT a RIGID body, it would fall towards the centre where potential is at minimum.

The shell model postulates that the shell is a rigid body, so it would not collapse, but I don't think Earth is completely rigid to resist such an enormous gravity

And for the sun it's obvious that plasma is no rigid body. Plasma particles move extremely fast which is a sort of pressure.

 

[Drakkith]

There was a study done you can google neutrons and gravity field.

But the idea of super dense matter , to me , implies changes to the atomic structure. There is a lot of empty space in an atom with the
Distance of the electrons and maybe even the space
Within a neutron or proton

Yes, I believe that the electron shells aren't at their minimum energy/size, as the atoms have thermal energy and such. Hence one of the reasons cooling a substance typically, but not always, causes contraction.

 

[DaveC426913]

Yes, I believe that the electron shells aren't at their minimum energy/size, as the atoms have thermal energy and such. Hence one of the reasons cooling a substance typically, but not always, causes contraction.

What? You seem to be suggesting that cooling a substance reduces the size of its atoms/electron shells, as opposed to reducing the space between atoms. I'd want that backed up.